Nonreciprocal devices in integrated optics

This article reviews the solutions that have been studied for the implementation of nonreciprocal devices in integrated optics. These components, either isolators or circulators, use the nonreciprocal interaction between light and a magnetic medium. The only two isolators that have been experimented on to date are described in detail with their advantages and drawbacks, and some solutions are proposed to overcome the difficulties encountered.     

Magneto-optical nonreciprocal phase shift in garnet/silicon-on-insulator waveguides

We demonstrate the integration of a single-crystal magneto-optical film onto thin silicon-on-insulator (SOI) waveguides by use of direct wafer bonding. Simulations show that the high confinement and asymmetric structure of SOI allows an enhancement of approximately 3x over the nonreciprocal phase shift achieved in previous designs; this value is confirmed by our measurements. Our structure will allow compact magneto-optical nonreciprocal devices, such as isolators, integrated on a silicon waveguiding platform.     

Nonreciprocal Transmission and Nonreciprocal Entanglement in a Spinning Microwave Magnomechanical System

This study presents nonreciprocal transmission and nonreciprocal magnon–phonon entanglement in a spinning microwave magnomechanical system. This system consists of microwave photons, magnon modes, and phonons. These are created by the vibrational mode of a yttrium iron garnet sphere. This investigation reveals that nonreciprocity is caused by the light that is circulating in a resonator that is experiencing a Fizeau shift. This leads to a difference in the effective detuning frequency of the photon for forwarding and backward drives. A super-strong transmission isolation rate (>100 dB) and a strong entanglement isolation rate (≈50 dB) are obtained by applying the experimental parameters. This scheme opens a new route for exploiting a variety of nonreciprocal effects, and it provides the theoretical basis for the design and realization of magnetically controllable isolators and diodes.     

Nonreciprocal coupling effects in gyrotropic waveguide structures

Nonreciprocal couplers in gyrotropic materials offer a new possibility for the realization of integrated optical isolators and circulators. This paper presents a theoretical analysis of such devices. We apply the finite-difference method and coupled mode as well as normal mode theory to neighbouring gyrotropic rib waveguides. Conclusions for the design of nonreciprocal devices are drawn.     

Suppressing the effect of disorders using time-reversal symmetry breaking in magneto-optical photonic crystals: An illustration with a four-port circulator

In integrated optical systems, nonreciprocal elements are indispensable devices that eliminate multi-path reflection between components. To miniaturizing these devices down to a single-wavelength scale, we study nonreciprocal effects in point defects of magneto-optical photonic crystals. The nonreciprocal effect splits degenerate mode pairs and its strength is maximized by spatially matching the magnetic domain pattern with a modal cross product. The resultant eigenmodes are a pair of counter-rotating states that lack time-reversal symmetry. Based upon these eigenmodes, we propose a micro-cavity four-port circulator constructed by coupling a magneto-optical cavity with two waveguides, where each rotating state supports light tunneling along a different direction. In the presence of strong magneto-optical couplings, due to time-reversal symmetry breaking, the performance of the isolator is fundamentally protected from the effect of small structural fluctuations. Numerical calculations demonstrate a four-port circulator with a 26 dB isolation and a roughness tolerance on the order of 0.1a, where a is the lattice constant of the crystal.     

Broadly tunable one-way terahertz plasmonic waveguide based on nonreciprocal surface magneto plasmons

One-way-propagating broadly tunable terahertz plasmonic waveguide at a subwavelength scale is proposed based on a metal-dielectric-semiconductor structure. Unlike other one-way plasmonic devices that are based on interference effects of surface plasmons, the proposed one-way device is based on nonreciprocal surface magneto plasmons under an external magnetic field. Theoretical and simulation results demonstrate that the one-way-propagating frequency band can be broadly tuned by the external magnetic fields. The proposed concept can be used to realize various high performance tunable plasmonic devices such as isolators, switches and splitters for ultracompact integrated plasmonic circuits.     

Asymmetric multimode interference isolator based on nonreciprocal phase shift

This paper presents an asymmetric multimode interference-based (MMI) optical isolator, by utilizing the magneto-optical nonreciprocal phase shift (NPS). Equivalent beam propagation method (BPM) simulation of symmetric and asymmetric isolators are performed using configuration of Air/Ce:YIG/SiO₂ on silicon substrate for integration. The asymmetric isolator is found to be much more compact in size and efficient in isolation compared with symmetric isolator. Simulation results show that the isolation of asymmetric structure is 23.8 dB higher than that of symmetric one. It is mainly because both symmetric mode and anti-symmetric mode are excited in asymmetric structure and hence can interfere destructively. The proposed device may play an important role in the optical communication systems and photonic integrated devices.     

Permeability tensor versus permittivity one in theory of nonreciprocal optical components

We discuss symmetry properties of the combined systems: electromagnetic field (TE and TM modes) + medium (nondiagonal permeability tensor [μ] and nondiagonal permittivity one [?]) in 2D photonic crystals with transverse magnetization. We show that the origin of orthogonality of the pairs (TE mode + [?]) and (TM mode + [μ]) is different parities of the corresponding fields with respect to the horizontal plane of symmetry of the crystal. As a result of this symmetry, a common use only of the permittivity tensor [?] in the electromagnetic theory of nonreciprocal optical components, ignoring the permeability tensor [μ], leads to loss of a significant part of possible solutions related to TE modes.     

Linear Optic Response of a Noncollinear Magnetic System: Hydrodynamic Theory

A hydrodynamic theory of the linear response of a noncollinearly magnetized medium interacting with electromagnetic radiation has been developed. Linear and quadratic magnetization effects caused by the spatial inhomogeneity of the magnetic moment have been analyzed. Linear magnetization effects include an effect similar to nonreciprocal birefringence, as well as reciprocal and nonreciprocal rotation of the plane of polarization, caused by the inhomogeneity of the magnetic moment. It has been shown that an effect caused by the equilibrium spin current can appear in the considered medium. This effect is determined either by the inhomogeneity of the spin current or by the spatial dispersion of a wave. The effect associated with the spatial dispersion of the wave is linear in its wave vector and is similar to nonreciprocal birefringence. The effect associated with the inhomogeneity of the spin current describes the rotation of the plane of polarization, which, however, can occur in the system with zero average magnetization.     

Modeling and simulation of polarization errors in Sagnac fiber optic current sensor

Sagnac fiber optic current sensor (S-FOCS) is a kind of optical interferometer based on Sagnac structure, optical polarization states of sensing light wave in Sagnac fiber optic current sensor are limited. However, several factors induce optical polarization error, and non-ideal polarized light waves cause the interference signal crosstalk in sensor, including polarizer, quarter-wave retarder, splice angular, birefringence and so on. With these errors, linearly polarized light wave in PM fiber and circularly polarized light wave in sensing fiber become elliptically polarized light wave, then, nonreciprocal phase shift induced by magnetic field of the current is interrupted by wrong polarization state. To clarify characteristics of optical polarization error in fiber optic current sensor, we analyze the evolution process of random optical polarization state, linear optical polarization state and circular optical polarization state in Sagnac fiber optic current sensor by using Poincare sphere, then, build optical polarization error models by using Jones matrix. Based on models of polarization state in Sagnac fiber optic current sensor, we investigate the influence of several main error factors on optical polarization error characteristics theoretically, including extinction ratio in polarizer, phase delay in quarter-wave retarder, splice angular between quarter-wave retarder and polarization maintaining fiber. Finally, we simulate and quantify nonreciprocal phase shift to be detected in fiber optic current sensor related with optical polarization errors. In the end, we demonstrate S-FOCS in test. The results show that transfer matrix errors are induced by inaccurate polarization properties during polarization state conversion, then, the stability and accuracy of the S-FOCS are affected, and it is important to control the polarization properties at each step of the polarization state conversion precisely.     

Asymmetric wave propagation in nonlinear systems

A mechanism for asymmetric (nonreciprocal) wave transmission is presented. As a reference system, we consider a layered nonlinear, nonmirror-symmetric model described by the one-dimensional discrete nonlinear Schr?dinger equation with spatially varying coefficients embedded in an otherwise linear lattice. We construct a class of exact extended solutions such that waves with the same frequency and incident amplitude impinging from left and right directions have very different transmission coefficients. This effect arises already for the simplest case of two nonlinear layers and is associated with the shift of nonlinear resonances. Increasing the number of layers considerably increases the complexity of the family of solutions. Finally, numerical simulations of asymmetric wave packet transmission are presented which beautifully display the rectifying effect.     

两段级联掺铒光纤放大器的优化研究

基于Giles模型,研究了980 nm和1480 nm泵浦的两段级联掺铒光纤放大器(EDFA)的设计,得出了掺铒光纤(EDF)的最佳长度和光隔离器的最佳位置随泵浦功率和信号功率的变化关系.比较980 nm和1480 nm泵浦的两段级联EDFA,可以发现,前者的最佳EDF长度短,而光隔离器最佳位置距EDFA输入端远.     

高功率法拉第隔离器多模退偏特性

理论分析了隔离器在高功率多模激光入射时的自退偏特性.结果表明：线性双折射致退偏与圆双折射致退偏均与入射光功率的平方成正比,线性双折射致退偏与光斑大小无关,而圆双折射致退偏随光斑半径的增大而减小.当光斑半径与旋转晶体半径相比很小时（R0/r0≥80）圆双折射引起的退偏大于线性双折射引起的退偏,当光斑半径接近旋转晶体半径（R0/r0≤3）时,与线性双折射引起的退偏相比,圆双折射引起的退偏可以忽略.对比单模激光入射,在同种条件下,多模入射使得线性双折射致退偏减小了0.4倍, 最小圆双折射致退偏减小为0.05倍.     

Nonreciprocal microwave transmission under the joint mechanism of phase modulation and magnon Kerr nonlinearity effect

Nonreciprocal microwave devices, in which the transmission of waves is non-symmetric between two ports, are indispensable for the manipulation of information processing and communication. In this work, we show the nonreciprocal microwave transmission in a cavity magnonic system under the joint mechanism of phase modulation and magnon Kerr nonlinearity effect. In contrast to the schemes based on the standard phase modulation or magnon Kerr nonlinearity, we find that the joint mechanism enables the nonreciprocal transmission even at low power and makes us obtain a high nonreciprocal isolation ratio. Moreover, when two microwave modes are coupled to the magnon mode via a different coupling strength, the presented strong nonreciprocal response occurs, and it makes the nonreciprocal transmission manipulating by the magnetic field within a large adjustable range possible, which overcomes narrow operating bandwidths. This study may provide promising opportunities to realize nonreciprocal structures for wave transmission.     

高功率法拉第隔离器多模退偏特性

理论分析了隔离器在高功率多模激光入射时的自退偏特性.结果表明:线性双折射致退偏与圆双折射致退偏均与入射光功率的平方成正比,线性双折射致退偏与光斑大小无关,而圆双折射致退偏随光斑半径的增大而减小.当光斑半径与旋转晶体半径相比很小时(R0/r0≥80)圆双折射引起的退偏大于线性双折射引起的退偏,当光斑半径接近旋转晶体半径(R0/r0≤3)时,与线性双折射引起的退偏相比,圆双折射引起的退偏可以忽略.对比单模激光入射,在同种条件下,多模入射使得线性双折射致退偏减小了0.4倍, 最小圆双折射致退偏减小为0.05倍.     

Perfect optical nonreciprocity in a double-cavity optomechanical system

Nonreciprocal devices are indispensable for building quantum networks and ubiquitous in modern communication technology. Here, we propose to take advantage of the interference between optomechanical interaction and linearly-coupled interaction to realize optical nonreciprocal transmission in a double-cavity optomechanical system. Particularly, we have derived essential conditions for perfect optical nonreciprocity and analysed properties of the optical nonreciprocal transmission. These results can be used to control optical transmission in quantum information processing.     

Polarization transformers for optical anisotropy: I. Nonreciprocal optical systems and the equivalence theorem

The problem of transformation of anisotropic properties of multipass nonreciprocal systems is considered. The equivalence theorem is generalized to the case of nonreciprocal elements (i.e., to elements that do not satisfy the equivalence theorem). It is shown that any nonreciprocal anisotropic phase element is equivalent to a combination of five elements, namely, a reciprocal linear phase plate, a nonreciprocal linear phase plate, a reciprocal rotator, and two Faraday rotators. The difference between reciprocal and nonreciprocal elements is considered from the viewpoint of their basis states.     

Iron-yttrium garnet films with magnetic vortices

Submicron iron-yttrium garnet films have been studied. The effect of the switching of nonreciprocal resonance absorption, which is caused by the switching of the polarization of vortices, has been revealed.     

Nonreciprocal transition between two indirectly coupled energy levels

We propose a theoretical scheme to realize nonreciprocal transition between two energy levels that can not coupled directly. Suppose they are coupled indirectly by two auxiliary levels with a cyclic four-level configuration, and the four transitions in the cyclic configuration are controlled by external fields. The indirectly transition become nonreciprocal when the time reversal symmetry of the system is broken by the synthetic magnetic flux, i.e., the total phase of the external driving fields through the cyclic four-level configuration. The nonreciprocal transition can be identified by the elimination of a spectral line in the spontaneous emission spectrum. Our work introduces a feasible way to observe nonreciprocal transition in a wide range of multi-level systems, including natural atoms or ions with parity symmetry.     

一维磁化等离子体光子晶体非互易特性研究

在理想条件下,为了研究等离子体回旋频率、等离子体频率、等离子体层厚度、周期常数和入射角在TM模式下对一维磁化等离子体光子晶体的非互易特性的影响,用利用传输矩阵法计算得到的TM波正向和反向传播的透射率来研究其非互易特性。研究结果表明,增加等离子体回旋频率和入射角度能够改善非互易特性;而一味地增加等离子体频率和等离子体层厚度将会使得非互易传播特性变得恶化;增加周期常数不能明显地改善非互易传播特性,但是通过改变外加磁场的施加方式能够改善其非互易特性。